The resulting dynamics between the two learning rules depend on the game under consideration as well as on the players' learning horizon. Fig. REF a shows the possible scenarios for the donation game. If the learning horizon is short, then learning rules are selected according to whether they result in an immediate advantage. As a result, we find that selfish learning is dominant, as one might expect. However, as players become increasingly patient, the dynamics first take the form of a bistable competition, and then FMTL becomes globally stable altogether. In this parameter regime, which starts after \(n\approx 60\)  learning steps, already a small initial fraction of FMTL is sufficient to drive selfish learning to extinction (Fig. REF b). Since clusters of FMTL learners perform better than clusters of selfish learners, the evolutionary advantage of FMTL is even more pronounced in structured populations [1]}, [2]} (see Methods for details).
<FIGURE>